The cylindrical bottle sells for $54.00, the conical bottle sells for $20.00 and the spherical bottle for $35. What is the best buy per cubic centimeter of perfume? Why?
*
To determine the best buy per cubic centimeter of perfume, we need to calculate the volume and price per cubic centimeter for each type of bottle.
The volume of a cylinder is calculated by the formula V = πr^2h, where π is a constant approximately equal to 3.14, r is the radius, and h is the height.
The volume of a cone is calculated by the formula V = (1/3)πr^2h.
The volume of a sphere is calculated by the formula V = (4/3)πr^3.
First, let's calculate the volume and price per cubic centimeter for the cylindrical bottle. Let's assume the radius of the cylindrical bottle is 4 cm and the height is 10 cm.
Volume of cylindrical bottle = π × 4^2 × 10 = 160π cm^3
Price per cubic centimeter of cylindrical bottle = $54.00 / 160π cm^3
Next, let's calculate the volume and price per cubic centimeter for the conical bottle. Let's assume the radius of the conical bottle is 3 cm and the height is 8 cm.
Volume of conical bottle = (1/3)π × 3^2 × 8 = 24π cm^3
Price per cubic centimeter of conical bottle = $20.00 / 24π cm^3
Finally, let's calculate the volume and price per cubic centimeter for the spherical bottle. Let's assume the radius of the spherical bottle is 5 cm.
Volume of spherical bottle = (4/3)π × 5^3 = 500π cm^3
Price per cubic centimeter of spherical bottle = $35.00 / 500π cm^3
Now, we can compare the price per cubic centimeter for each type of bottle.
For the cylindrical bottle: Price per cubic centimeter = $54.00 / 160π cm^3
For the conical bottle: Price per cubic centimeter = $20.00 / 24π cm^3
For the spherical bottle: Price per cubic centimeter = $35.00 / 500π cm^3
To determine the best buy per cubic centimeter of perfume, we need to find the lowest price per cubic centimeter among the three options. Thus, we would choose the bottle with the lowest price per cubic centimeter as the best buy.